Question

A disc of mass $2 \,kg$ and radius $0.2 \,m$ is rotating with angular velocity $30\,rad/s$. What is angular velocity, if a mass of $0.25\, kg$ is put on periphery of the disc?

• A. 24 rad/s
• B. 36 rad/s
• C. 15 rad/s
• D. 26 rad/s

Answer 1

Answer: (A)

If no external torque acts on a system of particles, then angular momentum of the system remains constant, that is
$ \tau =0 $
$ \Rightarrow \frac{dL}{dt}=0 $
$ \Rightarrow L=I \omega =$ constant
$ \Rightarrow I_1\omega_1=I_2\omega_2 $
hence $ \frac{1}{2}Mr^2\omega_1=\frac{1}{2}(M+2m)r^2\omega_2 $ .....(i)
Here $M=2\,Kg, m=0.25\,kg, r = 0.2\,m$,
$ \omega_1=30\,rad\,s^{-1} $
Hence, we get after putting the given values in Eq. (i)
$ \frac{1}{2}\times 2\times (0.2)^2 \times 30$
$=\frac{1}{2}\times (2 +2 \times 0.25)(0.2)^2\times \omega_2 $
or $ 1.2 =0.05 \omega_2 $
or $1.2=0.05 \omega_2 $
or $ \omega_2=24 \,rad \,s^{-1} $